In recent years, an optical transmission system of 40 Gbps or 100 Gbps has employed a digital coherent signal processing technique in which Dual Polarization-Quadrature Phase Shift Keying (DP-QPSK) modulation method is used. The digital coherent signal processing technique can, for example, improve the noise resistance and frequency usage efficiency and moreover achieve the long-distance transmission.
For example, when the phase of the carrier wave is estimated for extracting the symbol information out of received optical signals, a phase estimation circuit of an optical receiver having employed the digital coherent signal processing technique calculates the phase noise using a multiplication method. FIG. 12 is a block diagram illustrating an example of the phase estimation circuit. A phase estimation circuit 100 illustrated in FIG. 12 includes a phase estimation unit 101, a phase compensation unit 102, and a monitor unit 103. The phase estimation unit 101 estimates the phase θC of the carrier wave from a reception signal (θC+θS) including the phase θC of the carrier wave and the signal phase θS. Moreover, the phase estimation unit 101 calculates the phase noise by multiplying the reception signal. Then, the phase compensation unit 102 acquires the signal phase θS by removing the phase θC of the carrier wave including the phase noise from the reception signal (0C+OS) based on the estimated phase θC of the carrier wave and the calculated phase noise. The monitor unit 103 acquires the symbol information based on the signal phase θS acquired by the phase compensation unit 102.
Note that the multiplication method refers to a method of calculating the phase noise by multiplying by N, the reception signal modulated by the N-ary PSK method and moreover by dividing the N-multiplied signal into 1/N. FIG. 13 is an explanatory view illustrating an example of a process of a method of raising to the fourth power when the phase noise of the reception signal modulated by the QPSK method is calculated. In FIG. 13, in the case of the reception signal modulated by the QPSK method, in the constellation where the I component of the in-phase axis and the Q component of the quadrature axis are orthogonal, the signal points of quadrants are multiplied by four and the frequency of the four-multiplied signal is divided into ¼, whereby the phase noise is calculated.
Here, each reception signal modulated by the QPSK method is represented by e{j(ωt+θ)}. θ refers to the phase corresponding to each symbol of the QPSK, and specifically, there are four kinds of phases of the symbol: π/4, −π/4, 3π/4, and −3π/4. Raising each reception signal to the fourth power leads to Formula (1).(ej(ωt+θ))4=ej(4ωt+4θ)=ej(4ωt)ej(4θ)  (1)
Then, a specific value is assigned to θ in ej(4θ). In the case of θ=π/4, the symbol is ejπ=cos π+jsin π=−1. In the case of θ=−π/4, the symbol is e−jπ=cos(−π)+jsin(−π)=−1. In the case of θ=3π/4, the symbol is e3jπ=ejπ=−1. In the case of θ=−3π/4, the symbol is e−3jπ=e−jπ=−1.
In other words, all are summarized to −1 without depending on the symbol. Further, when the phase component θ that is different for every symbol is removed, just the noise component (ωt) remains. Then, the phase estimation unit 101 calculates the phase noise by integrating a predetermined number of noise components. Note that the estimation accuracy of the phase estimation circuit 100 largely depends on the number by which the biquadrate signal as the fourth power of the reception signal is multiplied. Therefore, in the method of raising to the fourth power, the phase estimation range within one quadrant is limited to ±45°, and when the phase has changed by 45° or more, the phase slip occurs out of the quadrant, in which case the deterioration in Bit Error Rate (BER) is caused.
In view of this, in order to reduce the frequency of the phase slip, more biquadrate signals are integrated to estimate the phase noise at higher accuracy. In other words, in the case of integrating more biquadrate signals, the average length of the phase estimation unit 101 needs to be longer. However, when the average length is too long, the biquadrate signals distribute more widely, so that the signal distributes from the quadrant to another adjacent quadrant; as a result, the estimation accuracy deteriorates. Therefore, the average length is not just set to be long simply but needs to be set to the appropriate length.
FIG. 14 is an explanatory view illustrating an example of the constellation of the QPSK method. In FIG. 14, the origin coordinates (I, Q) at which the Q component of the quadrature axis and the I component of the in-phase axis intersect are (0, 0). The symbol center coordinates X1 in a first quadrant A1 are (+0.5, +0.5), and the symbol center coordinates X2 in a second quadrant A2 are (−0.5, +0.5). The symbol center coordinates X3 in a third quadrant A3 are (−0.5, −0.5), and the symbol center coordinates X4 in a fourth quadrant A4 are (+0.5, −0.5).
The signal point of each symbol belongs to any one of the first quadrant A1, the second quadrant A2, the third quadrant A3, and the fourth quadrant A4, and the signal points distribute around the symbol center coordinates X1 to X4 of the quadrants A1 to A4. Therefore, each signal point is set in an ideal state as the point gets closer to the symbol center coordinates of each quadrant A1 to A4 because the BER is lower. In the actual optical transmission system, however, the transmission distance of the reception signal is long and the signal deterioration also occurs on the optical line, and the signal points distribute widely from the symbol center coordinates X1 to X4. The average length and the BER characteristic also change for every shape of the constellation, which is the set distribution of the signal points.
FIG. 15 is an explanatory view illustrating an example of the average length and the BER characteristic for every shape of the constellation. In the constellation “A” in FIG. 15, the shape of the constellation in each of the quadrants A1 to A4 is triangular, and the average length is short and the BER is high. In the constellation “B” in FIG. 15, the shape of the constellation in each of the quadrants A1 to A4 is circular, and the average length is optimum and the BER is low. In the constellation “C” in FIG. 15, the shape of the constellation in each of the quadrants A1 to A4 is a shape deformed to be close to a signal point of the adjacent quadrant, and the average length is long and the BER is high. Note that the shape of the constellation “C” is a donut-like shape when viewed across the entire quadrants A1 to A4 because the signal point in the quadrant is close to the signal point in another adjacent quadrant.
When the average length illustrated in FIG. 15 is focused, changing the average length can change the BER in addition to changing the shape of the constellation in each of the quadrates A1 to A4 to be the triangular shape, the circular shape, or the shape deformed to be close to the signal point of the adjacent quadrate.
In the optical receiver, the signal phase may change over time in accordance with the frequency deviation between the reception signal and the local oscillation signal, i.e., the frequency offset amount. In view of this, an offset compensation circuit that eliminates the frequency offset amount is disposed in the previous stage of the phase estimation circuit 100 in the optical receiver; however, a small amount of frequency offset remains, so that the phase noise is caused. Moreover, the optical transmission system has a plurality of sources of generating the phase noise on the optical line. As a result, under the influence of the phase noise, each signal point rotates around the origin coordinates (0, 0). The phase estimation circuit 100 removes the phase noise while checking the state of the signal point of each quadrant, and the update time interval is changed by changing the average length in the integration of the phase noise.
For example, when the time interval gets shorter, the average length becomes shorter and the amount of rotating around the origin coordinates also becomes smaller; as a result, the shape of the constellation becomes approximately triangular. On the contrary, when the time interval gets longer, the average length becomes longer and the amount of rotating around the origin coordinates becomes larger; as a result, the shape of the constellation becomes the shape deformed to be close to the signal point distribution of another adjacent quadrant. Therefore, it is necessary to optimize the average length for optimizing the time interval.
As a method of optimizing the average length, a method in which Error Vector Magnitude (EVM) is used is known. FIG. 16 are explanatory views illustrating an example of a method of selecting the average length of the QPSK method using EVM.
EVM refers to the method of calculating so that the distance from the symbol center coordinates of every quadrant to each signal point is minimized and selecting the optimal value. Since the constellation shape in FIG. 16A is triangular, the BER is high. Since the constellation shape in FIG. 16B is circular, the BER is low. Since the constellation shape in FIG. 16C is the shape deformed to be close to the signal point of the adjacent quadrant, the BER is high.
On this occasion, the EVM value of the constellation shape of FIG. 16C is higher than the EVM value of the constellation shape of FIG. 16A and FIG. 16B, and the BER of FIG. 16C is also higher than the BER of FIG. 16A and FIG. 16B. Therefore, when the EVM value is more than a predetermined value, the BER is also high; accordingly, the average length is shortened to set the optimal average length.
Japanese Laid-open Patent Publication No. 2011-166597
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Japanese Laid-open Patent Publication No. 2010-028795
However, in the constellation shape of FIG. 16A and FIG. 16B, since there is no difference in EVM value, it is impossible to distinguish the constellation shape between the triangular shape and the circular shape. As a result, the phase estimation unit 101 determines that, for example, the shape is circular and the BER is low although the constellation shape is triangular and the BER is high, in which case it is difficult to calculate the correct phase noise.